Abstract
In this article, we give a new simultaneous decomposition concerning the general matrix quaternity over an arbitrary division ring ℱ. A practical algorithm for the decomposition of the matrix quaternity is also presented. As applications, we establish some necessary and sufficient conditions for the existence of the general solutions to the systems of matrix equations
ACKNOWLEDGMENTS
This research was supported by the grants from the Ph.D. Programs Foundation of Ministry of Education of China (20093108110001), the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (09YZ13), Natural Science Foundation of China (60672160, 11171205), Singapore MoE Tier 1 Research Grant RG60/07, and Shanghai Leading Academic Discipline Project (J50101).
The authors would like to thank a referee very much for his or her valuable suggestions and comments, which resulted in a great improvement of the original manuscript.
Notes
Communicated by J.-T. Yu.